Translation of abstract (English)

Since the first star catalogues tremendous progress in the astrometric accuracy of positional observations has been achieved. In this thesis, I show how beneficial astrometric techniques are already today for the study of starburst clusters, and how astrometry will fundamentally improve our knowledge on exoplanets in the near future.
I first study two galactic starburst clusters, Westerlund 1 (Wd 1) and NGC 3603 YC, which are among the most massive young clusters in our Galaxy. I perform astrometric and photometric analyses of adaptive optics and Hubble Space Telescope observations of these clusters in order to understand on which time-scales these clusters formed. As a result, I derive upper limits for the age spreads of 0.4 Myr for the 4 to 5 Myr old cluster Wd 1, and 0.1 Myr for the 1 to 2 Myr old NGC 3603 YC. Thus, the star formation process in each of these clusters happened almost instantaneously.

The second part of this thesis deals with the dynamical properties and the initial mass function (IMF) of Wd 1. Astrometric analysis of multi-epoch, near-infrared adaptive optics observations of Wd 1 was used to distinguish the cluster's members from field stars. This lead to an unbiased determination of the internal velocity dispersion of the cluster, and an IMF slope of Gamma = -0.46 for the core of the cluster (R < 0.23 pc).

The final part of this thesis is devoted to the future prospects of detecting exoplanets with the GRAVITY instrument. The second-generation Very Large Telescope Interferometer instrument GRAVITY aims at achieving 10 μas accuracy. Here, I discuss the possibilities of detecting and characterizing exoplanets with masses down to a few Earth masses with the high sensitivity provided by GRAVITY, in addition to providing an initial target list.